On the Operator ℒ(f) = f log |f|

Journal of Functional Analysis

Volumn 169, Issue 2, 1999, Pages 391-420

  Iwaniec, Tadeusz ^a   Verde, Anne ^b  

^a SYRACUSE UNIVERSITY   (United States)

^b Dipartimento di Matematica e Applicazioni   (Italy)

Author keywords

Distributions; Hardy space; Jacobians

Indexed keywords

EID: 0000597622     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1999.3443     Document Type: Article

References (22)

1. 1 functions, in progress.
2. R. R. Coifman, P. L. Lions, Y. Meyer, and S. Semmes, Compensated compactness and Hardy spaces, J. Math. Pures Appl. 72 (1993), 247-286.
3. R. Coifman and R. Rochberg, Another characterization of BMO, Proc. Amer. Math. Soc. 79, No. 2 (1980), 249-254.
4. p-spaces of several variables, Acta Math. 129 (1972), 137-193.
5. L. Greco and T. Iwaniec, New inequalities for the Jacobian, Ann. Inst. H. Poincaré 11, No. 1 (1994), 17-35.
6. L. Greco, T. Iwaniec, and G. Moscariello, Limits of the improved integrability of the volume forms, Indiana Univ. Math. J. 44 (1995), 305-339.
7. Y. Gotoh, Remarks on multipliers for BMO on general domains, Kodai Math. J. 16 (1993), 79-89.
8. Y. Gotoh, On multipliers for BMOΦ on general domains, Ann. Acad. Sci. Fenn. Ser.A I Math. 19 (1994), 339-354.
9. T. Iwaniec, Integrability theory of the Jacobians, Lipschitz Lectures in Bonn, preprint, No. 36; Sonderforschungsbereich, Vol. 256, pp. 1-68, Bonn, 1995.
10. T. Iwaniec and C. Sbordone, On the integrability of the Jacobian under minimal hypothesis, Arch. Rational Mech. Anal. 119 (1992), 129-143.
11. T. Iwaniec and C. Sbordone, Weak minima of variational integrals, J. Reine Angew. Math. 454 (1994), 143-161.
12. T. Iwaniec and A. Verde, A study of Jacobians in Hardy-Orlicz spaces, Proc. Roy. Soc. Edinburgh 129A (1999), 539-570.
13. S. Janson, On functions with conditions on the mean oscillation, Ark. Mat. 14 (1976), 189-196.
14. F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415-426.
15. S. Müller, A surprising higher integrability property of mappings with positive determinant, Bull. Amer. Math. Soc. 21 (1989), 245-248.
16. E. Nakai, Pointwise multipliers for functions of weighted bounded mean oscillation, Studia Math. 105 (1993), 105-119.
17. E. Nakai and K. Yabuta, Pointwise multipliers for functions of bounded mean oscillation, J. Math. Soc. Japan 37 (1985), 207-218.
18. M. M. Rao and Z. D. Ren, "Theory of Orlicz Spaces," Dekker, New York, 1991.
19. D. Sarason, Functions of vanishing mean oscillation, Trans. Amer. Math. Soc. 207 (1975), 391-405.
20. E. M. Stein, Note on the class L log L (Theorem 2), Studia Math. 32 (1969), 305-310.
21. E. M. Stein, "Harmonic Analysis," Princeton Univ. Press, Princeton, NJ, 1993.
22. H. Wente, An existence theorem for surfaces of constant mean curvature, J. Math. Anal. Appl. 26 (1969), 318-344.